The above figures prove that what we studied in our good old school days is not totally right. 
Area of a  triangle                                 = (Base x Height) / 2 
Consider the First Triangle . 
Area of the whole triangle as a whole = (13 x 5) /2 = 32.5 square units 
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In the second triangle,

Area of Red Triangle                                  = (8 x 3)/2    =  12 square units 
Area of Green Triangle                               = (5x 2)/2     =   5 square units 
Area of rectangle                                         = 5x3           = 15 square units

(orange and green blocks together)        
                                                                                                                                      ----------------------------         
Total Area                                                                         =  32square units 

Where did 0.5 square units go ?